Free Printable Fundamental Mathematics 1A Review

1.

This law says that the sine of the angle divided by the length of the opposite side for each angle of triangle is equal.

a)

Cosine Law

b)

Tangent Law

c)

Pythagorean Theorem

d)

Sine Law

2.

∠A= 30°, b= 10, and ∠C= 15°, find ∠B and a.

a)

∠B = 45°, a = $\sqrt[]{2}$

b)

∠B = 90°, a = 5 $\sqrt[]{3}$

c)

∠B = 60°, a = 5

d)

∠B = 135°, a = 5 $\sqrt[]{2}$

3.

∠B= 60°, a= 23, and c= 33, find b.

a)

$\sqrt[]{21}$

b)

$\sqrt[]{22}$

c)

$\sqrt[]{23}$

d)

$\sqrt[]{24}$

4.

If sinθ = 14 , what is cosθ and tanθ?

a)

$\cos\theta\ =\ \pm\frac{\sqrt[]{15}}{5};\tan\theta=\sqrt[]{15}$

b)

$\cos\theta\ =\ \pm\sqrt[]{15};\tan\theta=\sqrt[]{15}$

c)

$\cos\theta\ =\ \pm\frac{\sqrt[]{15}}{4};\tan\theta=\frac{\sqrt[]{15}}{15}$

d)

$\cos\theta\ =\ \pm\frac{\sqrt[]{15}}{4}\ ;\tan\theta\ =\pm\ \frac{\sqrt[]{15}}{15}$

5.

Which of these is/are an example of a Pythagorean identities?

a)

$\sin^2\theta+\cos^2\theta=1$

b)

$1+\tan^2\theta=\sec^2\theta$

c)

$\cot^2\theta+1=\csc^2\theta$

d)

All of the above

6.

What is the reciprocal identity of cotθ?

a)

$\frac{1}{\cot\theta}$

b)

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

c)

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

d)

$\frac{1}{\tan\theta}$

7.

What is the addition formula for sin (s + t)?

a)

cos(s)cos(t) - sin(s)sin(t)

b)

sin(s)cos(t) + cos(s)sin(t)

c)

cos(s)sin(t) - sin(s)cos(t)

d)

sin(s)sin(t) + cos(s)cos(t)

8.

What is the subtraction formula for cos (s - t)?

a)

sin(s)sin(t) - cos(s)cos(t)

b)

cos(s + t)

c)

cos(s)cos(t) + sin(s)sin(t)

d)

cos(s)cos(t) - sin(s)sin(t)

9.

What is the double-angle identity formula for sin (2x)?

a)

sin(2x) = 2sin(x)cos(x)

b)

$\sin(2x)=\sin^2(x)+\cos^2(x)$

c)

$\sin(2x)=1-\sin^2(x)$

d)

$\sin(2x)=1-2\sin^2(x)$

10.

What is the double-angle identity formula for tan (2x)?

a)

$\tan\left(2x\right)=\frac{2\tan x}{1-\tan^2x}$

b)

$\tan\left(2x\right)=\frac{2\tan x}{1+\tan^2x}$

c)

$\tan\left(2x\right)=\frac{1-\cos\ 2x}{1-\tan^2x}$

d)

$\tan\left(2x\right)=\frac{1-\cos x}{1+\cos2x}$

11.

Half-angle identity for Sine:

a)

$\sin\left(\frac{u}{2}\right)=\pm\sqrt[]{\frac{1-\cos\ u}{2}}$

b)

$\cos\left(\frac{u}{2}\right)=\ \pm\sqrt[]{\frac{1+\cos\ u}{2}}$

c)

$\tan\left(\frac{u}{2}\right)=\frac{1-\cos\ u}{\sin\ u}$

d)

$\tan\left(\frac{u}{2}\right)=\frac{\sin\ u}{1+\cos u}$

12.

Half-angle identity for Tangent:

a)

$\sin\left(\frac{u}{2}\right)=\pm\sqrt[]{\frac{1-\cos\ u}{2}}$

b)

$\cos\left(\frac{u}{2}\right)=\ \pm\sqrt[]{\frac{1+\cos\ u}{2}}$

c)

$\tan\left(\frac{u}{2}\right)=\frac{1-\cos\ u}{\sin\ u}$

d)

$\tan\left(\frac{u}{2}\right)=\frac{\sin\ u}{1+\cos u}$

13.

Which of these are Product-Sum formulas?

a)

$\cos u+\cos v=2\cos\ \frac{u+v}{2}\cos\frac{u-v}{2}$

b)

$\cos u-\cos v=-2\sin\ \frac{u+v}{2}\sin\frac{u-v}{2}$

c)

$\sin u\cos v=\frac{1}{2}\left[\sin\left(u+v\right)+\sin\left(u-v\right)\right]$

d)

$\cos u\sin v=\frac{1}{2}\left[\sin\left(u+v\right)-\sin\left(u-v\right)\right]$

14.

Which of these are Sum-Product formulas?

a)

$\cos u+\cos v=2\cos\ \frac{u+v}{2}\cos\frac{u-v}{2}$

b)

$\cos u-\cos v=-2\sin\ \frac{u+v}{2}\sin\frac{u-v}{2}$

c)

$\sin u\cos v=\frac{1}{2}\left[\sin\left(u+v\right)+\sin\left(u-v\right)\right]$

d)

$\cos u\sin v=\frac{1}{2}\left[\sin\left(u+v\right)-\sin\left(u-v\right)\right]$

15.

What is cosine $0\degree$ ?

a)

0

b)

1

c)

$\frac{1}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

16.

What is cosine $30\degree$ ?

a)

0

b)

1

c)

$\frac{1}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

17.

What is sine $120\degree$ ?

a)

$-\frac{1}{2}$

b)

$-\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

18.

What is sine $135\degree$ ?

a)

$-\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{2}}{2}$

c)

$\frac{1}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

19.

What is $210\degree$ into radians?

a)

$\frac{5\pi}{6}$

b)

$\frac{3\pi}{2}$

c)

$\frac{11\pi}{6}$

d)

$\frac{7\pi}{6}$

20.

What is $270\degree$ into radians?

a)

$\frac{5\pi}{6}$

b)

$\frac{3\pi}{2}$

c)

$\frac{11\pi}{6}$

d)

$\frac{7\pi}{6}$

Fundamental Mathematics 1A Review

Total questions: 20

Worksheet time: 17mins

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