Daily Practice · Higher Plus
September 1953 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1953 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1953y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 2nd September 1953A cuboid measures 3 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd September 1953A 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?
- 4th September 1953A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 5th September 1953A car covers 580 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.
- 6th September 1953Work out the coordinates of the turning point of y = x^2 + 10x - 1.
- 7th September 1953y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 9.
- 8th September 1953A cuboid measures 11 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th September 1953A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th September 1953On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th September 1953Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 12th September 1953Simplify (x^2 + 3x - 40)/(x - 5).
- 13th September 1953A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 14th September 1953The 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.
- 15th September 1953A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 16th September 1953A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 17th September 1953Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
- 18th September 1953In an algebraic proof, how would you write an odd number in terms of an integer n?
- 19th September 1953y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 20th September 1953In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 21st September 1953The probability of winning a game is 5/8. A player expects 45 wins. How many games did they play?
- 22nd September 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd September 1953A rectangle is 5 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th September 1953Make x the subject of 5x + 5 = y(x + 5).
- 25th September 1953y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 26th September 1953In a vector proof you find that vector PQ = 3a - 5b and vector RS = 12a - 20b. What does this show about PQ and RS?
- 27th September 1953A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 28th September 1953A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 29th September 1953Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 30th September 1953Write 2/(x - 5) + 4/(x - 4) as a single fraction.