Daily Practice · Higher Plus
April 1985 5-a-day
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The batch download puts all 5 tiers' April 1985 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1985A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 2nd April 1985Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 3rd April 1985Simplify (x^2 - 1)/(x - 1).
- 4th April 1985y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 5th April 1985In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 6th April 1985The probability of winning a game is 1/2. A player expects 48 wins. How many games did they play?
- 7th April 1985On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th April 1985A block has mass 610 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th April 1985In an algebraic proof, how would you write an even number in terms of an integer n?
- 10th April 1985y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 11th April 1985In a vector proof you find that vector PQ = 3a - 5b and vector RS = 12a - 20b. What does this show about PQ and RS?
- 12th April 1985A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 13th April 1985A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 14th April 1985x = 132 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th April 1985Make x the subject of 7x + 5 = y(x + 5).
- 16th April 1985y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 25.
- 17th April 1985A cuboid measures 13 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th April 1985A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th April 1985On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th April 1985A car covers 690 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st April 1985Write 5/(x + 2) + 2/(x - 6) as a single fraction.
- 22nd April 1985A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd April 1985A cuboid measures 7 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th April 1985A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th April 1985A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 26th April 1985Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 27th April 1985Solve 12x^2 - x - 6 = 0.
- 28th April 1985y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 29th April 1985The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 30th April 1985A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.