Daily Practice · Higher Plus
April 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1983 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1983Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 2nd April 1983Solve x^2 + 3x + 2 < 0.
- 3rd April 1983y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 4th April 1983A cuboid measures 11 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th April 1983A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th April 1983On 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?
- 7th April 1983Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).
- 8th April 1983Write x^2 - 10x + 9 in the form (x + a)^2 + b.
- 9th April 1983A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 10th April 1983The 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.
- 11th April 1983A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 12th April 1983A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 13th April 1983A rectangle is 15 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th April 1983Work out the coordinates of the turning point of y = x^2 + 10x + 8.
- 15th April 1983y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 16th April 1983In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 17th April 1983The probability of winning a game is 3/5. A player expects 18 wins. How many games did they play?
- 18th April 1983On 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?
- 19th April 1983Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 20th April 1983Simplify (x^2 + 2x - 48)/(x - 6).
- 21st April 1983y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 22nd April 1983In a vector proof you find that vector PQ = 4a - 6b and vector RS = 20a - 30b. What does this show about PQ and RS?
- 23rd April 1983A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 24th April 1983A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 25th April 1983A block has mass 890 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th April 1983In an algebraic proof, how would you write an odd number in terms of an integer n?
- 27th April 1983y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 28th April 1983A cuboid measures 8 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th April 1983A 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?
- 30th April 1983On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?