Daily Practice · Higher Plus
April 1981 5-a-day
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The batch download puts all 5 tiers' April 1981 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1981y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 2nd April 1981In a vector proof you find that vector PQ = 3a - 6b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 3rd April 1981A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 4th April 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th April 1981x = 98 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th April 1981The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 7th April 1981y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 8th April 1981A cuboid measures 3 cm by 6 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th April 1981A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th April 1981A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 11th April 1981A car covers 130 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.
- 12th April 1981A quadratic sequence starts 7, 13, 25, 43. Work out the second difference, and the coefficient of n^2.
- 13th April 1981y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 16.
- 14th April 1981A cuboid measures 4 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th April 1981A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th April 1981On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th April 1981Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 18th April 1981Solve x^2 - 5x + 6 > 0.
- 19th April 1981A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 20th April 1981The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 21st April 1981A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 22nd April 1981A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 23rd April 1981Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 24th April 1981Write x^2 + 6x + 1 in the form (x + a)^2 + b.
- 25th April 1981y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 26th April 1981In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 27th April 1981The probability of winning a game is 3/4. A player expects 27 wins. How many games did they play?
- 28th April 1981On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th April 1981A rectangle is 30 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th April 1981Work out the coordinates of the turning point of y = x^2 - 12x - 11.