Daily Practice · Higher Plus
September 1961 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1961 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1961y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 2nd September 1961The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 3rd September 1961A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 4th September 1961On 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?
- 5th September 1961Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 6th September 1961Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 7th September 1961y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 8th September 1961In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 9th September 1961The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 10th September 1961A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 11th September 1961A block has mass 540 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th September 1961f(x) = 3x - 3 and g(x) = 3x - 1. Work out fg(4).
- 13th September 1961y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 16.
- 14th September 1961In a vector proof you find that vector PQ = 5a + 5b and vector RS = 25a + 25b. What does this show about PQ and RS?
- 15th September 1961A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 16th September 1961On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th September 1961x = 72 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th September 1961The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 19th September 1961A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 20th September 1961A cuboid measures 3 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st September 1961A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd September 1961A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 23rd September 1961A car covers 500 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.
- 24th September 1961A quadratic sequence starts 0, 11, 30, 57. Work out the second difference, and the coefficient of n^2.
- 25th September 1961y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 26th September 1961A cuboid measures 11 cm by 12 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th September 1961A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th September 1961On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th September 1961Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 30th September 1961Solve x^2 + 14x + 48 < 0.