Daily Practice · Higher Plus
April 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1986 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1986The probability of winning a game is 4/5. A player expects 44 wins. How many games did they play?
- 2nd April 1986On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd April 1986Simplify sqrt(48) + sqrt(3), giving your answer in the form a sqrt(b).
- 4th April 1986Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 5th April 1986y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 6th April 1986In a vector proof you find that vector PQ = 6a + 6b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 7th April 1986A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 8th April 1986A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 9th April 1986A rectangle is 22 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th April 1986f(x) = 5x + 8 and g(x) = 5x + 8. Work out fg(4).
- 11th April 1986y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 49.
- 12th April 1986A cuboid measures 9 cm by 10 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th April 1986A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th April 1986On 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?
- 15th April 1986Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 16th April 1986The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 17th April 1986A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 18th April 1986A cuboid measures 7 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th April 1986A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th April 1986A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 21st April 1986A block has mass 330 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd April 1986A quadratic sequence starts 8, 25, 50, 83. Work out the second difference, and the coefficient of n^2.
- 23rd April 1986y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 24th April 1986The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 25th April 1986A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 26th April 1986On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th April 1986x = 192 and y = 70, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th April 1986Solve x^2 + 8x < 0.
- 29th April 1986y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 30th April 1986In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.