Daily Practice · Higher Plus
May 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1984Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 2nd May 1984The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 3rd May 1984y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 4th May 1984The 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.
- 5th May 1984A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 6th May 1984On 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?
- 7th May 1984A block has mass 350 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th May 1984A quadratic sequence starts 9, 16, 29, 48. Work out the second difference, and the coefficient of n^2.
- 9th May 1984y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 10th May 1984In 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.
- 11th May 1984The probability of winning a game is 2/5. A player expects 18 wins. How many games did they play?
- 12th May 1984A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 13th May 1984x = 178 and y = 137, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th May 1984Solve x^2 - 4x < 0.
- 15th May 1984y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 16th May 1984In a vector proof you find that vector PQ = 5a - 3b and vector RS = 25a - 15b. What does this show about PQ and RS?
- 17th May 1984A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 18th May 1984On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th May 1984A car covers 530 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th May 1984Write x^2 - 4x - 8 in the form (x + a)^2 + b.
- 21st May 1984A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd May 1984A cuboid measures 5 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd May 1984A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th May 1984A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 25th May 1984Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 26th May 1984Work out the coordinates of the turning point of y = x^2 - 2x - 7.
- 27th May 1984y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 28th May 1984A cuboid measures 8 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th May 1984A bag holds 3 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th May 1984On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st May 1984Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).