Module 1 Questions Secti Secti on 1 – Basic Basic Numbers and Patterns
Complete the following: 1) 2) 3) Write down all of the factors of 96. 4) Write down the highest common factor of the following numbers: 36, 108 and 216. State the next two numbers in the following patterns: 5) 1, 3, 6, 10, 15, 21 6) 1, 8, 27, 64, 125, 216
Secti Secti on 2 – – Fractions, Fractions, Decimals & Percentages Percentages
Write the following fractions with the denominator stated: 1)
With denominator 96
Reduce the following fractions to their lowest terms:
5) 3)
2) With denominator 35
6) 4)
Arrange the following sets of fractions in order of size from smallest to largest
7)
8)
Complete the following fractions, cancelling where possible:
11) 13) 9)
15)
Convert the following fractions into decimals:
19)
12) 14) 10)
16)
17)
18)
Write down the values of the following: 20) 3.196 + 2.475 + 18.369 22) 26.31 x 3.901 24) 0.76 x 0.38 26) 50 ÷ 0.125
21) 19.36 + 2.36 - 5.931 + 0.001 23) 1.369 x 9.631 25) 0.169 ÷ 0.00013 27) 0.001024 ÷ 0.032
28)
Write the following numbers in standard form and to 3 significant fi gures 29) 256 987 012 30) 0.00002369841 0.00002369841 31) 13 694.2269 32) 0.000 000 100 1 1
Convert the following decimals into fractions: 33) 0.025
34) 1.875
35) 0.0625 Find the difference between the following:
36)
37)
38)
and 0.82916 Convert the following into a percentage: 39)
̇
and 0.7103 40)
41) 0.6832 42) 1.3982 Solve the following: 43) What is 20% of 90? 44) What is 17.5% of £150? 45) Given that 13.3cm is 15% of a length, what is half of the le ngth? 46) If 69.25m is 20%, then how long is 51.2%? 47) State the quotient, dividend and divisor in the following equation:
– Ratio, Proportion and Measures Secti on 3
1) Five friends each race in order to contribute to charity in the ratio of 12:8:9:1:2. If the sum total was £554.24, how much was contributed by each part? 2) A line is 840mm long. If the line is split into three parts of ratio 2:7:11; calculate the length of each part, 3) A team of 6 engineers repair an aeroplane in 11 hours 30 minutes. How long would it take the team to repair the plane if there were 8 engineers? Give your answer to the nearest minute. 4) The FDR of an aeroplane has strength of 80% at a distance of 1.25km. At 2.00km, the strength of the signal falls by 48.75%. How far away would the FDR be if the signal strength is 25% if the signal strength decreases as the square of the distance increases? 5) List the 10 standard fundamental measurements stating their SI unit. Write the approximate equivalent values for the following: 6) 2.2lbs in kg 7) 30 inches in feet 8) 2 stone in ounces 9) 1 UK pint in litres 10) 26.2°C in Fahrenheit 11) 31.75 F in Kelvin Secti on 4 – Logarithms and Antilogarithms Using Tables Only
Find the logarithms of the following numbers: 1) 23 2) 9.1 3) 125.1 4) 0.002 5) 36.98 6) 0.0000031426 7) 10 8) 1369241 9) If log10 50.3 = 1.7016, state which figures represent the characteris tic and the mantissa.
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Find the antilogarithms of the following numbers: 10) 3.41
11) 0.026
12) 7.11
13)
14)
15) 1.1111
16) 2.699 18)
17)
19)
√
Secti on 5 – Using Square and Square Root Tables
Find values for the following: 1) 5.32 3) 7.368 2 5) 0.112 7) 6042
√ 11) √ 13) √ 15) √ 9)
2) 8.822 4) 1362.92 6) 0.00008432 8) 49.012
√ 12) √ 14) √ 16) √ 10)
Secti on 6 – Basic Algebra and Equations
Simplify the following: 1) 3)
Factorise fully:
4) 2)
5) 6) 7) 8) 9) 10) 11) State the values of x which satisfy the equation in questions 6 to 10. Solve the following sets of simultaneous equations:
13) 14) 15) 16) 17) Find the points of intersection of the line and the circle with the equation . Rearrange the following equations: 18) for R. 19) for r. 20) for ε . 21) ⁄ for R. 12)
0
3
22)
for Q.
23)
for v. ()
Secti on 7 – Numbers and Number systems
Complete the following indices: 1) 3) Complete the following using the number system stated: 5) Transfer 101101 2 to denary. 7) 4728 to denary 9) 1011110001 2 to octal. 11) 457.953125 10 to binary. 13) 1100101 2 + 100101 2 15) ABC16 + EF16.
2) 4)
6) 10001111.12 to denary. 8) 112F16 to denary. 10) 1011111101001 2 to hexadecimal 12) 3768 to hexadecimal. 14) 110100012 – 1012 16) 871 8 + 427 8
– Volumes, Surface Area, Graphs and the Equation y = mx + c Secti on 8
1) A trapezium has parallel sides of 7cm and 13cm. The vertical height is 10cm. What is the total area of this shape? 2) If the volume of a sphere is 4188.79mm3. What is the length of the diameter? 3) In the cone shown, find the surface area and the volume. Find the area of the following shapes: 5cm 4) 3m 1m 0.5m
8cm
2m 17.5mm
5)
396km
19.4mm
45km
6) 412km
7) The volume of a small copper cylinder is 180cm 3. If the radius of the cylinder is 25mm, what is the height of the cylinder? State the equations of the following straight lines when: 8) The two coordinates (2, 14) and (7, 34) lie on the line. 9) The line intersects the y axis at 3 and the point (-3, 6) is on the line. 10) The points A and B are perpendicular to C and D. If the two lines intersect at the midpoint of CD with coordinates (2, -6) and CD has the equation what is the equation of the line AB?
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Secti on 9 – Circles, Radians and Similar and Congruent Triangles
Find the missing angles in the following circles: 1) 2) x
y
3) C
47°
A
40° 60°
B A
50°
Convert the following angular measurements into their equivalent radian measure: 4) 270° 5) 156° 6) 39°06’ 7) 60° 8) 361° 9) 100° Convert the following radian measures to their angular equivalents: 10)
radians
radians 13) radians
11)
12) 1 radian
14) 2π 15) 10π 16) A sector has radii of length 5m and the angle subtended is 15°. What is the length of the arc? 17) The diagram shows a straight path of 70m from town A to town Railway Track B. A railway track, in an arc shape, whose centre is C, also runs 70m A B between the towns and has a radius of 44m. Calculate the 44m 44m following: (a) The magnitude of angle ACB. (b) The length of the C railway track. (c) The shortest distance from C to the path. (d) The area of the region bounded by the railway track and the path. 18) In the triangles below, find the missing sides in triangle PQR without using Y trigonometry: Q 55°
12.97cm P
7.44cm
35° 8.62cm R X
10.63cm
Z
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Secti on 10 – Pythagoras’ Theorem, Trigonometry and Polar Coordinates
Using the tables only, find the following values: 1) Sin 36° 2) Sin 14°30’ 3) Sin 89°01’ 4) Sin 3°49’ -1 5) Sin 0.4554 6) Sin -1 0.010 7) Sin-1 0.8642 8) Sin -1 0.6631 9) Cos 69° 10) Cos 44°35’ 11) Cos 35°10’ 12) Cos 26°22’ -1 13) Cos 0.3364 14) Cos -10.2497 15) Cos-10.1 16) Cos-10.4554 17) Tan 39° 18) Tan 28°06’ 19) Tan 84°59’ 20) Tan 35°35’ -1 21) Tan 0.5987 22) Tan -1 2.669 23) Tan-1 15.39 24) Tan -1 0.0017 Using Pythagoras’ Theorem, calculate: 25) The hypotenuse when the two shorter sides are of length 12m and 5m. 26) The adjacent side when the hypotenuse is 25km and the opposite is 15km. 27) Complete the following table for equivalent angles when 0°≤θ≤360°. θ Sin θ Cos θ Tan θ 108° 207° 134° 300° 286° 95° 163° Calculate the polar coordinates for the following: 28) (3, 2) 29) (8, -7) 30) (-3, -5) 31) (12, -5) Calculate the polar coordinates for the following but state the angle in radians: 32) (2, 1) 33) (-6, 8) 34) (-2, -4) 35) (4, -7) Calculate the Cartesian coordinates for the following polar points: 36) (5, 30°) 37) (3, 330°) 38) (7, 65°) 39) (5, π/3) 40) (6, 3π/4) 41) (10, 5π/3)
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