Daily Practice · Higher Plus
September 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1963 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1963x = 193 and y = 125, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd September 1963The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 3rd September 1963y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 36.
- 4th September 1963In a vector proof you find that vector PQ = 6a + b and vector RS = 24a + 4b. What does this show about PQ and RS?
- 5th September 1963A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 6th September 1963On 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?
- 7th September 1963A car covers 500 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.
- 8th September 1963A quadratic sequence starts 3, 14, 31, 54. Work out the second difference, and the coefficient of n^2.
- 9th September 1963A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 10th September 1963A cuboid measures 14 cm by 10 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th September 1963A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th September 1963A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 13th September 1963Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 14th September 1963Solve x^2 + 10x + 16 > 0.
- 15th September 1963y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 16th September 1963A cuboid measures 6 cm by 14 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th September 1963A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th September 1963On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th September 1963Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 20th September 1963Write x^2 - 4x - 15 in the form (x + a)^2 + b.
- 21st September 1963y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 22nd September 1963The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 23rd September 1963A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 24th September 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 25th September 1963A rectangle is 19 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th September 1963Work out the coordinates of the turning point of y = x^2 + 6x + 10.
- 27th September 1963y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 16.
- 28th September 1963In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 29th September 1963The probability of winning a game is 1/2. A player expects 12 wins. How many games did they play?
- 30th September 1963On 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?