National 5 (Scotland) · National 5 Mathematics

Trigonometry, Vectors, Statistics and Applications

37 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 37 questions

What is the period of the graph $y = cos 3 x^{\circ}$ ?
The graph of $y = sin x^{\circ}$ is transformed to give $y = sin (x + 40)^{\circ}$ . What is the transformation?
What is the exact value of $tan 6 0^{\circ}$ ?
Simplify $5 - 5 cos^{2} x$ .
Solve $2 sin x^{\circ} = 1$ for $0 \leq x \leq 360$ .
Solve $3 cos x^{\circ} + 1 = 0$ for $0 \leq x \leq 360$ , to 1 decimal place.
In a triangle, two sides are 7 cm and 9 cm with an included angle of $6 0^{\circ}$ . Find the third side to 1 decimal place.
A triangle has sides 5 cm, 6 cm and 7 cm. Find its largest angle, to 1 decimal place.
In a triangle, $A = 4 0^{\circ}$ , $B = 6 5^{\circ}$ and the side opposite $A$ is 8 cm. Find the side opposite $B$ , to 1 decimal place.
In triangle PQR, $P Q = 10$ cm, angle $P = 4 0^{\circ}$ and angle $Q = 7 5^{\circ}$ . Find the length of QR to 1 decimal place.
Find the area of a triangle with sides 9 cm and 12 cm and an included angle of $5 0^{\circ}$ , to 1 decimal place.
A ship sails 10 km on a bearing of $07 0^{\circ}$ . How far east has it travelled, to 1 decimal place?
The bearing of B from A is $06 5^{\circ}$ . What is the bearing of A from B?
Find the magnitude of the vector $(3 - 4)$ .
$a = (2 - 1)$ and $b = (- 3 5)$ . Find $2 a - b$ .
Find the magnitude of the 3D vector $2 - 3 6$ .
ABCD is a parallelogram with $A B = u$ and $A D = v$ . Express $B D$ in terms of $u$ and $v$ .
£2500 is invested at 3% per year compound interest. What is it worth after 4 years?
A car worth £14 000 loses 15% of its value each year. What is it worth after 3 years, to the nearest penny?
After a 20% increase a price is £90. What was the original price?
Calculate $\frac{2}{3} \div \frac{4}{9}$ .
Calculate $2 \frac{1}{4} - 1 \frac{5}{6}$ .
Find the standard deviation of 4, 6, 8, 10, 12, using the sample formula, to 2 decimal places.
Find the semi-interquartile range of 3, 5, 6, 8, 9, 12, 14, 15.
Class A and Class B both have a mean test mark of 62. Class A has a standard deviation of 4 and Class B has 11. Which statement is correct?
A line of best fit on a scatter graph has equation $y = 2.4 x + 10$ . Predict $y$ when $x = 15$ .
Increase 480 by 12.5%.
Solve $3 (2 x - 1) = 5 x + 4$ .
Solve $\frac{x + 1}{2} = \frac{2 x - 3}{3}$ .
Make $r$ the subject of $V = \frac{1}{3} π r^{2} h$ .
Simplify $3 (a + 2 b) - 2 (a - b)$ .
A phone plan costs £12 a month plus 5p per megabyte. How much does it cost in a month when 140 MB are used?
Where does the line $y = - 3 x + 7$ cross the $x$ -axis?
Calculate $\frac{6 \times 1 0 ^{8}}{1.5 \times 1 0 ^{3}}$ , giving the answer in scientific notation.
A solid is made from a cone of radius 3 cm and height 4 cm sitting on a hemisphere of radius 3 cm. Find the total volume in terms of $π$ .
Three adult tickets and two child tickets cost £47. Two adult tickets and five child tickets cost £57. What is the price of a child ticket?
The line $y = 2 x - 3$ is drawn on a diagram. Which of these points lies on the line?

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