Daily Practice · Higher Plus
September 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1959 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1959A cuboid measures 3 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd September 1959A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd September 1959On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th September 1959Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 5th September 1959Use the iteration x(n+1) = cube root of (9x(n) + 6) with x(0) = 4. Work out x(1) to 3 decimal places.
- 6th September 1959A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 7th September 1959A cuboid measures 11 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th September 1959A bag holds 5 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th September 1959A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 10th September 1959Simplify sqrt(20) + sqrt(80), giving your answer in the form a sqrt(b).
- 11th September 1959Work out the nth term of the quadratic sequence 3, 9, 19, 33, ...
- 12th September 1959y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 13th September 1959The 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.
- 14th September 1959A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 15th September 1959On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th September 1959A rectangle is 22 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th September 1959The point (3, 2) lies on y = f(x). Write down its image on y = f(x) + 2.
- 18th September 1959y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 19th September 1959In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 20th September 1959The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 21st September 1959A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 22nd September 1959Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 23rd September 1959Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 24th September 1959y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 81.
- 25th September 1959In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 26th September 1959A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 27th September 1959On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th September 1959A block has mass 230 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th September 1959f(x) = 6x - 9 and g(x) = 5x + 4. Work out fg(6).
- 30th September 1959A train slows steadily from 36 m/s to rest in 10 seconds. Work out its deceleration.