Free Printable FORMATIVE TEST : Add Math Form 3 Semester 2 2021

1.

Choose the correct law of logarithms

a)

\log\ a\ -\ \log\ b\ =\log\ \left(a-b\right)

b)

$\frac{\log a}{\log b}=\log\ \left(\frac{a}{b}\right)$

c)

$\log\ a\ -\log b=\log\ \left(\frac{a}{b}\right)$

d)

$\left(\log\ a\right)\cdot\left(\log\ b\right)=\log\left(ab\right)$

2.

Expand the following logarithm:

\log_b\ \left(\frac{x^3y}{z^2}\right)

a)

$\log_b2x+\log_by-\log_b3z$

b)

$2\log_bx+\log_by-3\log_bz$

c)

$3\log_bx+\log_by-2\log_bz$

d)

$3\log_bx-\log_by-2\log_bz$

3.

Write the expression $\log4-\log2+2\log6$

as a single logarithm. Then simplify if possible.

a)

$\log98$

b)

$\log48$

c)

$\log72$

d)

$\log14$

4.

If $2^x=y$ , which of the following is true?

a)

$\log_2y=x$

b)

$\log_2x=y$

c)

$\log_xy=2$

d)

$\log_y2=x$

5.

Solve for x: $\log\left(2x-1\right)-\log5=2$ .

x=_{ }

?

a)

26.7

b)

167.0

c)

250.5

d)

-203

6.

Find value of the following $\log_225\times\log_5\sqrt{64}$

a)

3

b)

4

c)

5

d)

6

7.

What would the change base look like for:

$\log_927$

a)

$\log3$

b)

$\frac{\log9}{\log27}$

c)

$\frac{\log27}{\log9}$

d)

$\ln3$

8.

Solve $\ln\left(5x+2\right)=15$ by using natural logarithms. Give the answer in three decimal places.

a)

3269015.075

b)

3269017.372

c)

3269019.372

d)

653803.075

9.

Given $\log_{2\ }3=t$ , express $\log_{9\ }2$ in terms of t.

a)

$\frac{2}{t}$

b)

$\frac{1}{2t}$

c)

$\frac{t}{2}$

d)

$2t$

10.

Which of the following graph shows a graph of linear relation?

a)

b)

c)

d)

11.

Based on the graph, find the gradient and Y-intercept.

a)

$m=\frac{4}{3},c=\frac{9}{4}$

b)

$m=\frac{3}{4},c=\frac{9}{4}$

c)

$m=-\frac{3}{4},c=\frac{15}{4}$

d)

$m=\frac{3}{4},c=\frac{15}{4}$

12.

From the line of best fit in the diagram, find the value of y when x = 2.5.

a)

0.640

b)

4.365

c)

0.450

d)

2.818

13.

The diagram shows part of a straight line that represents graph of line of best fit. Express Y in terms of X.

a)

$\frac{1}{y}=\frac{6}{7}x^2-\frac{16}{3}$

b)

$y=\frac{6}{7}x^2-\frac{3}{16}$

c)

$\frac{1}{y}=\frac{7}{6}x^2-\frac{16}{3}$

d)

$y=\frac{7}{6}x^2-\frac{16}{3}$

14.

The diagram shows part of a straight line that represents graph of line of best fit. Express Y in terms of X.

a)

$y=\frac{1}{2}x+\frac{2}{x}$

b)

$x+y=2x^2+\frac{1}{2}$

c)

$x+y=\frac{1}{2}x^2+2$

d)

$y=\frac{1}{2x^2}+2$

15.

The diagram shows part of a straight line that represents graph of line of best fit. Express Y in terms of X.

a)

$\frac{y}{x^{\left(-\frac{1}{2}\right)}}=-\frac{3}{4}x+\frac{13}{2}$

b)

$\left(\frac{y}{x}\right)^{\frac{1}{2}}=-\frac{3}{4}x+\frac{13}{2}$

c)

$\frac{y}{\sqrt{x}}=-\frac{3}{4}x+\frac{13}{2}$

d)

$\left(\frac{y}{x}\right)^{\frac{1}{2}}=\frac{3}{4x}-\frac{13}{2}$

16.

Convert the non-linear equation y = 3x² − 4 to linear equation.

a)

$\frac{y}{x}=3x-\frac{4}{x}$

b)

$\frac{y}{x}=3x^3-\frac{4}{x}$

c)

$y=3x-\frac{4}{x^2}$

d)

$\frac{y}{x^2}=3-\frac{4}{x^2}$

17.

Based on the diagram, there is a point that plotted wrongly. What is the point?

a)

A

b)

B

c)

C

d)

D

18.

Based on the graph of line of best fit below, predict the value of log₁₀ y when log₁₀ x = 100.

a)

$10$

b)

$\frac{1}{10}$

c)

$100$

d)

$\frac{1}{100}$

19.

Based on the graph, find the value of y when $\frac{1}{x}=0.5$ .

a)

3.7

b)

7.4

c)

14.8

d)

3.75

20.

Based on the graph, calculate the value of $\frac{1}{v}$ when $\frac{1}{u}$ = 0.

a)

0.1

b)

10

c)

1

d)

0.01

21.

Which of the following represents the gradient of two perpendicular straight lines?

a)

$m_1=\frac{1}{m_2}$

b)

$m_1=m_2$

c)

$m_1m_2=-1$

d)

$m_1=-m_2$

22.

Given two straight lines y = 3x − 2 and y = 2 + 3x. Both of the lines are

a)

perpendicular to each other.

b)

same.

c)

parallel to each other.

d)

reciprocal to each other.

23.

State the gradient of a straight line that is perpendicular to 2y = 3x + 6.

a)

$-\frac{2}{3}$

b)

$\frac{2}{3}$

c)

$\frac{3}{2}$

d)

$-\frac{3}{2}$

24.

Find the equation of a straight line that perpendicular to the straight line x = 5 − 2y and passes through point (−2, 9).

a)

$2y=-x+13$

b)

$y=2x+13$

c)

$2y=x-13$

d)

$y=-2x-13$

25.

Find the equation of a straight line that parallel to the straight line x + 4y −8 = 0 and passes through the midpoint of P(9, 5) and Q(−3, 7).

a)

$4y=-x+27$

b)

$y=4x-6$

c)

$4y=-x+8$

d)

$y=-4x+18$

26.

Find the area of a triangle where A, B and C is

(5, 10), (2, 1) and (8, 3) respectively.

a)

48

b)

24

c)

−24

d)

−48

27.

The diagram shows a triangle ABC. Find the area of triangle ABC.

a)

-24

b)

24

c)

−12

d)

12

28.

The diagram shows a quadrilateral ABCD. Find the area of quadrilateral ABCD.

a)

11.5

b)

22

c)

28

d)

10

29.

Find the value of k if points A(2, 3), B(4, k) and

C(6, −3) is collinear.

a)

3

b)

2

c)

1

d)

0

30.

The diagram shows a triangle ABC. Given the area of the triangle is 9 units², find the value of h.

a)

7

b)

6

c)

5

d)

4

31.

Write $2^{-4}=\frac{1}{16}$ in logarithmic equation.

a)

$\log_2\left(\frac{1}{16}\right)=-4$

b)

$\log_{-4}2=\frac{1}{16}$

c)

$\log_{-4}\left(\frac{1}{16}\right)=2$

d)

$\log_{2x}\left(-4\right)=\frac{1}{16}$

32.

Given log₅(4x − 7) = log₅(x + 5).

Find the value of x.

a)

3

b)

4

c)

7

d)

12

33.

Evaluate log₃81.

a)

$4$

b)

$-4$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

34.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

35.

Evaluate log_b(b)⁴

a)

1

b)

0

c)

4

d)

b

36.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

37.

A is the point (2, 3) and B is the point (7, -5).

Find the equation of the line through A that is perpendicular to AB.

Give your answer in the form y = mx+c.

a)

$y=\frac{5}{8}x+\frac{7}{4}$

b)

$y=-\frac{5}{8}x+\frac{7}{4}$

c)

$y=\frac{7}{4}x+\frac{5}{8}$

38.

The equation of the line L IS y = −2x + 6,

Find the equation of the line perpendicular to line L that passes through (9, 3).

a)

y = 0.5x +1.5

b)

y = 0.5x −1.5

c)

y = -0.5x −1.5

39.

Convert y = ax^b into the form Y = mX + c. State the expression of Y.

a)

log x

b)

log y

c)

log a

d)

log b

40.

a)

h = 2/3 k= 8/3

b)

h = 2/3 , k= 16/3

c)

h = 8/3, k = 2/3

d)

h = 16/3 , k = 2/3

FORMATIVE TEST : Add Math Form 3 Semester 2 2021

Total questions: 40

Worksheet time: 59mins

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