Daily Practice · Higher Plus
May 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1963In 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.
- 2nd May 1963The probability of winning a game is 1/8. A player expects 9 wins. How many games did they play?
- 3rd May 1963A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 4th May 1963A car covers 160 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th May 1963The point (5, -6) lies on y = f(x). Write down its image on y = f(x - 1).
- 6th May 1963y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 25.
- 7th May 1963In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 8th May 1963A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 9th May 1963On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th May 1963Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 11th May 1963Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 12th May 1963A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
- 13th May 1963A cuboid measures 3 cm by 6 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th May 1963A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th May 1963A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 16th May 1963Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 17th May 1963f(x) = 2x + 2 and g(x) = 6x - 4. Work out fg(3).
- 18th May 1963y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 19th May 1963A cuboid measures 6 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th May 1963A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st May 1963On 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?
- 22nd May 1963A rectangle is 8 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd May 1963The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 24th May 1963y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 25th May 1963The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 26th May 1963A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 27th May 1963A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 28th May 1963Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 29th May 1963A quadratic sequence starts 12, 22, 36, 54. Work out the second difference, and the coefficient of n^2.
- 30th May 1963y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 25.
- 31st May 1963In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.