Daily Practice · Higher Plus
April 1971 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1971 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1971A cuboid measures 4 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd April 1971A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd April 1971A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 4th April 1971x = 87 and y = 62, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th April 1971Write x^2 + 4x - 13 in the form (x + a)^2 + b.
- 6th April 1971y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 7th April 1971A cuboid measures 6 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th April 1971A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th April 1971On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th April 1971A car covers 120 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.
- 11th April 1971Work out the coordinates of the turning point of y = x^2 + 12x + 8.
- 12th April 1971y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 13th April 1971The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 14th April 1971A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 15th April 1971A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 16th April 1971Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 17th April 1971Simplify (x^2 - 5x - 6)/(x + 1).
- 18th April 1971y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 19th April 1971In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 20th April 1971The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 21st April 1971On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd April 1971Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 23rd April 1971In an algebraic proof, how would you write an even number in terms of an integer n?
- 24th April 1971A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 25th April 1971In a vector proof you find that vector PQ = a + 6b and vector RS = 2a + 12b. What does this show about PQ and RS?
- 26th April 1971A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 27th April 1971A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 28th April 1971A rectangle is 12 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th April 1971Make x the subject of 6x + 2 = y(x + 2).
- 30th April 1971y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.