NBT Toets 4

Question 1 of 20

1

\(\sqrt{4x^{16}}\)=

Select one of the following:

\(2x^4\)
\(2x^8\)
\(\pm 2x^4\)
\(\pm 2x^8\)

Explanation

Question 2 of 20

1

Die grafiek van \(y=2^x\) word eers in die \(y\)-as, en die resultaat in die lyn \(y=x\) gereflekteer. Die grafiek wat so ontstaan is \(y=\)

The graph of \(y=2^x\)is first reflected in the line \(y\)-axis, and the result in the line \(y=x\) . The graph that is formed is \(y=\)

Select one of the following:

\(-2^x\)
\(2^{-x}\)
\(log_2 x\)
\(log_\frac{1}{2} x\)

Explanation

Question 3 of 20

1

Die waardes van/ The values of \(x\) waarvoor / for which\(logx \leq 0\)

Select one of the following:

\(x<0\)
\(x \leq 1\)
\(0<x \leq 1\)
\(x \geq 1\)

Explanation

Question 4 of 20

1

Watter van die volgende reekse konvergeer:
Which of the following will converge:

Select one of the following:

\(4+\frac{4}{3}+\frac{4}{9}\)
4 + 8 + 16 +...
4 + 2 + 0+ ...
4 + 3,5 + 2 + ...

Explanation

Question 5 of 20

1

'n Boom is 2 m hoog. Dit groei elke jaar \(\frac{3}{4}\) van die vorige jaar se hoogte. Wat is die hoogste wat dit kan word?

A tree is 2 m high. It grows each year with \(\frac{3}{4}\) of the previous year's length. What is the highest that it can become?

Select one of the following:

6 m
7 m
8 m
9 m

Explanation

Question 6 of 20

1

Beskou die ry:/ Determine the sequence: 1; 2; 3; 4; 5; 8; ... Die 30'ste term is:/ The 30'th term will be:

Select one of the following:

59
1073741824
14
32768

Explanation

Question 7 of 20

1

Vir watter waardes van \(x\) sal die reeks \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ konvergeer:

For which values of \(x\) will the series \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ converge::

Select one of the following:

\(-1<x<1\)
\(\frac{-3}{2}<x<\frac{-1}{2}\)
\(-3<x<1\)
\(-2<x<3\)

Explanation

Question 8 of 20

1

Sannie spaar elke maand \(x\) rand in 'n rekening, rentekoers \(i\).p.j, maandeliks. Sy doen dit vir 25 jaar. Daarna los sy die geld in die rekening vir 'n verdere 5 jaar. 'n Formule waarmee die waarde van die rekening bepaal kan word, is

Sannie saves \(x\) rand in an account every month, interest rate \(i\), p.j, monthly. She has been doing this for 25 years. Then she leaves the money in the account for another 5 years. A formula for determining the value of the account is

Select one of the following:

\(\frac{x(1+i)^{25}-1}{i}(1+i)^5\)
\(\frac{x(1+i)^{300}-1}{i}(1+i)^5\)
\(\frac{x(1+i)^{25}-1}{i}(1+i)^{60}\)
\(\frac{x(1+i)^{300}-1}{i}(1+i)^{60}\)

Explanation

Question 9 of 20

1

Bepaal die waarde van/ Determine the value of \(\sum\limits_{k=2}^{10} (5k-2)\)

Select one of the following:

280
252
255
229,5

Explanation

Question 10 of 20

1

Skryf die volgende in sigma notasie: 6+3+0+⋯ vir \(n\) terme.

Write the following in sigma notation: 6+3+0+⋯ vir \(n\) terms.

Select one of the following:

\(\sum \limits_{k=1}^{n} (9-3k)\)
\(\sum \limits_{k=1}^{n} (9-3n)\)
\(\sum \limits_{k=1}^{n} (\frac{k}{2}(15-3k))\)
\(\sum \limits_{k=1}^{n} (\frac{k}{2}(9-3n))\)

Explanation

Question 11 of 20

1

Watter stelling is onwaar:/ Which statement is not true:

Select one of the following:

As al drie hoeke van 'n driehoek ooreenstemmend gelyk is aan al drie hoeke van 'n ander driehoek, dan is die driehoeke gelykvormig. / If all three angles of a triangle are equal to all three angles of another triangle, then the triangles are similar.
As al die sye van 'n driehoek ooreenstemmend eweredig is met al drie sye van 'n ander driehoek, dan is die driehoeke gelykvormig. / If all the sides of a triangle are equaly proportional to all three sides of another triangle, then the triangles are similar.
Alle gelykvormige driehoeke is ook kongruent./ All similar triangles are also congruent.
Alle kongruente driehoeke is ook gelykvormig./ All congruent triangles are also similar

Explanation

Question 12 of 20

1

Die identiteit \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) sal ongefinieerd wees in die interval \(-90^\circ \leq x\leq 90^\circ\)

Theidentity \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) will be undefined in the interval \(-90^\circ \leq x\leq 90^\circ\)

Select one of the following:

\(45^\circ\)
\(-45^\circ\)
\(45^\circ\) of \(-45^\circ\)
oral gedefinieerd/ everywhere defined

Explanation

Question 13 of 20

1

Hoeveel oplossings sal die vergelyking \(2sinx.cosx=\frac{1}{2}\) in die interval \(-90^\circ \leq x\leq 90^\circ\) hê?

How many solutions will the equation \(2sinx.cosx=\frac{1}{2}\) have in the interval \(-90^\circ \leq x\leq 90^\circ\) ?

Select one of the following:

0
1
2
4

Explanation

Question 14 of 20

1

Watter van die volgende is twee moontlike oplossings van \(sin^2x-cos^2x=\frac{1}{2}\)

Which of the following are two possible solutions of \(sin^2x-cos^2x=\frac{1}{2}\)

Select one of the following:

\(\pm60^\circ\)
\(\pm30^\circ\)
\(\pm45^\circ\)
\(\pm150^\circ\)

Explanation

Question 15 of 20

1

Bepaal die waarde van/ Determine the value of \(sin195^\circ\)

Select one of the following:

\(\frac{\sqrt{2}-\sqrt{6}}{4}\)
\(\frac{-\sqrt{2}+\sqrt{6}}{4}\)
\(\frac{\sqrt{2}+\sqrt{6}}{4}\)
\(\frac{-\sqrt{2}-\sqrt{6}}{4}\)

Explanation

Question 16 of 20

1

As \(sin12°cos12°=\frac{2}{5}\) , dan is tan24°=

If\(sin12°cos12°=\frac{2}{5}\) , then tan24°=

Select one of the following:

\(\frac{\sqrt{6}}{12}\)
\(\frac{4}{3}\)
\(\frac{\sqrt{21}}{2}\)
\(\frac{2}{21}\)

Explanation

Question 17 of 20

1

As tanθ=0,75 en cosθ<0, bepaal die waarde van sin2θ.

Iftanθ=0,75 andcosθ<0,determine the value of sin2θ.

Select one of the following:

\(\frac{6}{5}\)
\(\frac{8}{5}\)
\(\frac{24}{25}\)
1,5

Explanation

Question 18 of 20

1

Bereken/ Calculate QR

Select one of the following:

48,09
10,083
13,09
24

Explanation

Question 19 of 20

1

99 Getalle se gemiddeld is 101. As 90 van hierdie getalle se gemiddeld 100 is, wat is die gemiddeld van die ander 9 getalle?

The average of 99 numbers is 101. If 90 of these numbers' average is 100, what is the average of the other 9 numbers?

Select one of the following:

102
121
111
100

Explanation

Question 20 of 20

1

Die grafieke \(y=f(x)\) en \(y=g(x)\) sny by \(A(\frac{-3}{2};\frac{-9}{4})\) en B(2;3). Dit sny die asse soos aangetoon. Vir watter waardes van \(x\) sal \(f(x).g(x)≤0\) ?

The graphs \(y=f(x)\) and\(y=g(x)\) intersect at \(A(\frac{-3}{2};\frac{-9}{4})\) and B(2;3). It cuts the axes as shown. For which values of \(x\) will \(f(x).g(x)≤0\) ?

Select one of the following:

\(\frac{-3}{2}≤x≤2\)
\(\frac{-3}{2}≤x≤3\)
\(x≤\frac{-3}{2}\) of \(x≥2\)
\(-1≤x≤0\) of \(x≥3\)

	Created by Rika Grobler over 10 years ago

Toets om te help met nbt toetse

NBT Toets 4

Question 1 of 20

\(\sqrt{4x^{16}}\)=

Select one of the following:

Explanation

Question 2 of 20

Die grafiek van \(y=2^x\) word eers in die \(y\)-as, en die resultaat in die lyn \(y=x\) gereflekteer. Die grafiek wat so ontstaan is \(y=\) The graph of \(y=2^x\)is first reflected in the line \(y\)-axis, and the result in the line \(y=x\) . The graph that is formed is \(y=\)

Select one of the following:

Explanation

Question 3 of 20

Die waardes van/ The values of \(x\) waarvoor / for which\(logx \leq 0\)

Select one of the following:

Explanation

Question 4 of 20

Watter van die volgende reekse konvergeer: Which of the following will converge:

Select one of the following:

Explanation

Question 5 of 20

'n Boom is 2 m hoog. Dit groei elke jaar \(\frac{3}{4}\) van die vorige jaar se hoogte. Wat is die hoogste wat dit kan word? A tree is 2 m high. It grows each year with \(\frac{3}{4}\) of the previous year's length. What is the highest that it can become?

Select one of the following:

Explanation

Question 6 of 20

Beskou die ry:/ Determine the sequence: 1; 2; 3; 4; 5; 8; ... Die 30'ste term is:/ The 30'th term will be:

Select one of the following:

Explanation

Question 7 of 20

Vir watter waardes van \(x\) sal die reeks \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ konvergeer: For which values of \(x\) will the series \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ converge::

Select one of the following:

Explanation

Question 8 of 20

Select one of the following:

Explanation

Question 9 of 20

Bepaal die waarde van/ Determine the value of \(\sum\limits_{k=2}^{10} (5k-2)\)

Select one of the following:

Explanation

Question 10 of 20

Skryf die volgende in sigma notasie: 6+3+0+⋯ vir \(n\) terme. Write the following in sigma notation: 6+3+0+⋯ vir \(n\) terms.

Select one of the following:

Explanation

Question 11 of 20

Watter stelling is onwaar:/ Which statement is not true:

Select one of the following:

Explanation

Question 12 of 20

Die identiteit \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) sal ongefinieerd wees in die interval \(-90^\circ \leq x\leq 90^\circ\) Theidentity \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) will be undefined in the interval \(-90^\circ \leq x\leq 90^\circ\)

Select one of the following:

Explanation

Question 13 of 20

Hoeveel oplossings sal die vergelyking \(2sinx.cosx=\frac{1}{2}\) in die interval \(-90^\circ \leq x\leq 90^\circ\) hê? How many solutions will the equation \(2sinx.cosx=\frac{1}{2}\) have in the interval \(-90^\circ \leq x\leq 90^\circ\) ?

Select one of the following:

Explanation

Question 14 of 20

Watter van die volgende is twee moontlike oplossings van \(sin^2x-cos^2x=\frac{1}{2}\) Which of the following are two possible solutions of \(sin^2x-cos^2x=\frac{1}{2}\)

Select one of the following:

Explanation

Question 15 of 20

Bepaal die waarde van/ Determine the value of \(sin195^\circ\)

Select one of the following:

Explanation

Question 16 of 20

As \(sin12°cos12°=\frac{2}{5}\) , dan is tan24°= If\(sin12°cos12°=\frac{2}{5}\) , then tan24°=

Select one of the following:

Explanation

Question 17 of 20

As tanθ=0,75 en cosθ<0, bepaal die waarde van sin2θ. Iftanθ=0,75 andcosθ<0,determine the value of sin2θ.

Select one of the following:

Explanation

Question 18 of 20

Bereken/ Calculate QR

Select one of the following:

Explanation

Question 19 of 20

99 Getalle se gemiddeld is 101. As 90 van hierdie getalle se gemiddeld 100 is, wat is die gemiddeld van die ander 9 getalle? The average of 99 numbers is 101. If 90 of these numbers' average is 100, what is the average of the other 9 numbers?

Select one of the following:

Explanation

Question 20 of 20

Select one of the following:

Explanation

Die grafiek van \(y=2^x\) word eers in die \(y\)-as, en die resultaat in die lyn \(y=x\) gereflekteer. Die grafiek wat so ontstaan is \(y=\)

The graph of \(y=2^x\)is first reflected in the line \(y\)-axis, and the result in the line \(y=x\) . The graph that is formed is \(y=\)

Watter van die volgende reekse konvergeer:
Which of the following will converge:

'n Boom is 2 m hoog. Dit groei elke jaar \(\frac{3}{4}\) van die vorige jaar se hoogte. Wat is die hoogste wat dit kan word?

A tree is 2 m high. It grows each year with \(\frac{3}{4}\) of the previous year's length. What is the highest that it can become?

Vir watter waardes van \(x\) sal die reeks \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ konvergeer:

For which values of \(x\) will the series \(1+\frac{1+x}{2}+\frac{\left( 1 + x \right)^{2}}{4}\)+⋯ converge::

Skryf die volgende in sigma notasie: 6+3+0+⋯ vir \(n\) terme.

Write the following in sigma notation: 6+3+0+⋯ vir \(n\) terms.

Die identiteit \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) sal ongefinieerd wees in die interval \(-90^\circ \leq x\leq 90^\circ\)

Theidentity \(\frac{cos2x}{(cosx+sinx)^3}=\frac{cosx-sinx}{sin2x}\) will be undefined in the interval \(-90^\circ \leq x\leq 90^\circ\)

Hoeveel oplossings sal die vergelyking \(2sinx.cosx=\frac{1}{2}\) in die interval \(-90^\circ \leq x\leq 90^\circ\) hê?

How many solutions will the equation \(2sinx.cosx=\frac{1}{2}\) have in the interval \(-90^\circ \leq x\leq 90^\circ\) ?

Watter van die volgende is twee moontlike oplossings van \(sin^2x-cos^2x=\frac{1}{2}\)

Which of the following are two possible solutions of \(sin^2x-cos^2x=\frac{1}{2}\)

As \(sin12°cos12°=\frac{2}{5}\) , dan is tan24°=

If\(sin12°cos12°=\frac{2}{5}\) , then tan24°=

As tanθ=0,75 en cosθ<0, bepaal die waarde van sin2θ.

Iftanθ=0,75 andcosθ<0,determine the value of sin2θ.

99 Getalle se gemiddeld is 101. As 90 van hierdie getalle se gemiddeld 100 is, wat is die gemiddeld van die ander 9 getalle?

The average of 99 numbers is 101. If 90 of these numbers' average is 100, what is the average of the other 9 numbers?