Free Printable Diagnostic Test in Math 10

1.

It is a polynomial equation of degree two that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

a)

Linear Equation

b)

Linear Inequality

c)

Quadratic Equation

d)

Quadratic Inequality

2.

Which of the following is a quadratic equation?

a)

2r²+4r-1

b)

3t-7=12

c)

s²+5s-14=0

d)

2x²-7x≥3

3.

In the quadratic equation 3x²+7x-4=0, which is the quadratic term?

a)

x

b)

7x

c)

3x²

d)

-4

4.

Which of the following is in standard form?

a)

x²-8x=15

b)

x³+4x+1=0

c)

x²=105

d)

2x²-3x-20=0

5.

It is a method in solving quadratic equations by looking for the factors of the terms.

a)

Solving QE by extracting the square root

b)

Solving QE by factoring

c)

Solving QE by quadratic formula

d)

Solving QE by discriminant

6.

It is a method in solving quadratic equations when you have to get the half of the second term then square it then add it to the equation.

a)

Solving QE by extracting the square root

b)

Solving QE by factoring

c)

Solving QE by quadratic formula

d)

Solving QE by completing the square

7.

Which of the following is the formula for quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$x=\frac{b\pm\sqrt{b^2-4ac}}{2a}$

c)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{a}$

d)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2}$

8.

It is used to find the number of real root and also the nature of the roots of a quadratic equation

a)

Linear Equation

b)

Discriminant

c)

Quadratic Equation

d)

Nature of the Roots

9.

Which of the following is the value of the discriminant of the equation 2r²+4r-1?

a)

24

b)

7

c)

23

d)

8

10.

Is it possible for the value of the discriminant to be equal to zero?

a)

yes

b)

no

c)

sometimes

d)

i don't know

11.

Find the value of the discriminant of the equation 2w²+7w-3=0

a)

70

b)

71

c)

72

d)

73

12.

Find the value of the discriminant of the equation $\frac{4}{3}w^2+w=192$

a)

-1025

b)

1025

c)

0

d)

5/2

13.

What is the nature of the root if the value of the discriminant is < 0?

a)

Real

b)

Real and Equal

c)

Real and Unequal

d)

Not Real

14.

(1,2) (2,3) (3,4) (4,5) (5,6) Plot the given points and determine the type of graph it represents

a)

Linear Function

b)

Quadratic Function

c)

Cubic Function

d)

Quartic Function

15.

If the value of a in the standard form of quadratic function is negative it means that:

a)

the parabola is opening upwards

b)

the parabola is opening downwards

c)

It doesn’t mean anything

d)

It will never happen

16.

If a is greater than 0, the behavior of the graph of the quadratic function is

a)

opening downwards

b)

opening upwards

c)

opening to the left

d)

opening to the right

17.

the vertex form of quadratic function is given by $y=a\left(x-h\right)^2+k$
what is the equation of symmetry?

a)

x=y

b)

x=k

c)

x=h

d)

x=a

18.

What is the simplified form of $4^0\times5^{-2}\times6^{-1}\times100^0\ \times\frac{1}{2^{-1}}$ ?

a)

1

b)

$\frac{1}{75}$

c)

$\frac{1}{150}$

d)

$\frac{1}{6000}$

19.

Which of the following is true?

a)

$5^{\frac{1}{2}}+5^{\frac{1}{3}}=5^5$

b)

$\frac{2^{\frac{1}{2}}}{2^{\frac{1}{3}}}=2^{\frac{2}{9}}$

c)

$\left(3^{\frac{1}{3}}\right)^2=9^{\frac{2}{3}}$

d)

$4^{-\frac{2}{3}}=\frac{1}{4^{\frac{2}{3}}}$

20.

What is the equivalent of the image below using exponential notation?

a)

$4^{\frac{1}{3}}+2^{\frac{1}{5}}$

b)

$4^3+2^5$

c)

$6^8$

d)

$6^{\frac{1}{8}}$

21.

Which of the following radical equations will have x=6 as the solution?

a)

$\sqrt{x}-2x+7$

b)

$\sqrt{2x-3}=x-3$

c)

$\sqrt{x}=9$

d)

$3\sqrt{x}=5$

22.

What is the result after simplifying $2\sqrt{3}+4\sqrt{3}-5\sqrt{3}$

a)

$-\sqrt{3}$

b)

$\sqrt{3}$

c)

$11\sqrt{3}$

d)

$21\sqrt{3}$

23.

$\left(2\sqrt{8}+3\sqrt{5}\right)\left(6\sqrt{8}+7\sqrt{5}\right)$

Which of the following is the result when we simplify

a)

$12\sqrt{64}+14\sqrt{40}+18\sqrt{40}+21\sqrt{25}$

b)

$12\sqrt{8}+32\sqrt{40}+21\sqrt{5}$

c)

$201+64\sqrt{10}$

d)

$195\sqrt{10}$

24.

$\frac{6-\sqrt{2}}{4-3\sqrt{2}}$

What is the result when we simplify

a)

$5$

b)

$-2\sqrt{2}$

c)

$5-\sqrt{2}$

d)

$-9-7\sqrt{2}$

25.

What is the simplified form of

a)

$\sqrt{3}$

b)

c)

$\sqrt{27}$

d)

26.

Which of the following is an incorrect characteristic of a radical in simplest form?

a)

No fraction as radicands

b)

No radicands with variable

c)

No radical appears in the denominator of a fraction

d)

No radicands have perfect square factors than 1

27.

$2√3,-5√2,\ 10√3,\ 14√2\ and-3√2$

What is the sum of

a)

$34\sqrt{5}$

b)

$18\sqrt{5}$

c)

$6\sqrt{2}+12\sqrt{3}$

d)

$12\sqrt{2}+6\sqrt{3}$

28.

$\left(2+\sqrt{5}\right)\left(5-\sqrt{7}\right)$

Which of the following is the simplified form of

a)

$10+2\sqrt{5}$

b)

$10+7\sqrt{5}-\sqrt{35}$

c)

$10+3\sqrt{7}-\sqrt{35}$

d)

$10-2\sqrt{7}+5\sqrt{5}-\sqrt{35}$

29.

$\frac{\sqrt{20x+5}}{\sqrt{5x}}$

What is the simplified form of

a)

$\sqrt{4x^2+x}$

b)

$5x\sqrt{4x^4+x}$

c)

$\frac{5x\sqrt{4x^4+x}}{x}$

d)

$\frac{\sqrt{4x^2+x}}{x}$

30.

These are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.

a)

Trigonometric Identities

b)

Trigonometry

c)

Oblique Triangles

d)

Law of Sine

31.

With respect to the given angle, what is the ratio of the hypotenuse to the opposite side?

a)

sine

b)

cosine

c)

tangent

d)

cosecant

32.

These are triangles that do not have a right angle

a)

30 x 60 x 90

b)

45 x 45 x 90

c)

obese triangles

d)

oblique triangles

33.

It is defined as the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

a)

Law of Cosine

b)

Heron's Formula

c)

Law of Sine

d)

Trigonometric Identities

34.

Which of the following is true about the formula of Law of Cosine?

a)

It can be interchanged

b)

It can be used if the given are one side and one angle only.

c)

It can be used to find an angle given 2 sides and the angle opposite one of them.

d)

It can be used to find an angle given three sides.

35.

Which of the following statements is correct?

a)

x=8

b)

$\sin\ 30\degree=\frac{1}{x}$

c)

$\sin\ 60\degree=\frac{y}{4}$

d)

$\cos60\degree=\frac{4}{y}$

36.

Given the figure, which refers to the angle of depression?

a)

$\angle MKN$

b)

$\angle MKL$

c)

$\angle LKN$

d)

none of these

37.

if p=30 and q=60, what is the measure of $\angle R$

a)

$40\degree$

b)

$55\degree$

c)

$60\degree$

d)

$65\degree$

38.

Find the value of side c to the nearest unit

a)

20

b)

21

c)

22

d)

24

39.

In the right triangle PQR, PQ=12 cm and QR = 5cm. What is cos R?

a)

$\frac{12}{13}$

b)

$\frac{5}{13}$

c)

$\frac{5}{12}$

d)

$\frac{12}{5}$

40.

Determine which of the following identities is incorrect.

a)

$\cos\theta=\frac{1}{\csc\theta}$

b)

$\sin\theta=\frac{1}{\csc\theta}$

c)

$\csc\theta=\frac{1}{\sin\theta}$

d)

$\sec\theta=\frac{1}{\cos\theta}$

Diagnostic Test in Math 10

Total questions: 40

Worksheet time: 20mins

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