Daily Practice · Higher Plus
April 1975 5-a-day
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The batch download puts all 5 tiers' April 1975 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1975Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 2nd April 1975Write 4/(x + 3) + 5/(x + 5) as a single fraction.
- 3rd April 1975A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 4th April 1975In a vector proof you find that vector PQ = a + 3b and vector RS = 3a + 9b. What does this show about PQ and RS?
- 5th April 1975A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 6th April 1975A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 7th April 1975A block has mass 480 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th April 1975Solve 6x^2 - 17x + 5 = 0.
- 9th April 1975y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 10th April 1975A cuboid measures 6 cm by 11 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th April 1975A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th April 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th April 1975x = 122 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th April 1975f(x) = 5x + 7. Work out the inverse function f^-1(x).
- 15th April 1975y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 16th April 1975A cuboid measures 13 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th April 1975A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th April 1975A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 19th April 1975A car covers 600 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th April 1975Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 21st April 1975y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 16.
- 22nd April 1975The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 23rd April 1975A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 24th April 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th April 1975Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 26th April 1975Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 4. Work out x(1) to 3 decimal places.
- 27th April 1975A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 28th April 1975In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 29th April 1975The probability of winning a game is 1/2. A player expects 44 wins. How many games did they play?
- 30th April 1975A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?