Daily Practice · Higher Plus
April 1984 5-a-day
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The batch download puts all 5 tiers' April 1984 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1984x = 127 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd April 1984Use the iteration x(n+1) = cube root of (6x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.
- 3rd April 1984A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 4th April 1984The 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.
- 5th April 1984A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 6th April 1984A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 7th April 1984A car covers 500 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th April 1984Work out the nth term of the quadratic sequence 8, 12, 20, 32, ...
- 9th April 1984y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 10th April 1984In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 11th April 1984The probability of winning a game is 3/10. A player expects 39 wins. How many games did they play?
- 12th April 1984On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th April 1984Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 14th April 1984The point (2, 0) lies on y = f(x). Write down its image on y = f(-x).
- 15th April 1984y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 16th April 1984In a vector proof you find that vector PQ = 2a - 4b and vector RS = 10a - 20b. What does this show about PQ and RS?
- 17th April 1984A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 18th April 1984A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 19th April 1984Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 20th April 1984Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 21st April 1984y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 36.
- 22nd April 1984A cuboid measures 9 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd April 1984A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th April 1984On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th April 1984A rectangle is 20 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th April 1984f(x) = 4x + 5 and g(x) = 6x + 3. Work out fg(2).
- 27th April 1984A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
- 28th April 1984A cuboid measures 6 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th April 1984A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th April 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?