Daily Practice · Higher Plus
September 1967 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1967 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1967The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 2nd September 1967A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 3rd September 1967A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 4th September 1967A block has mass 880 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th September 1967In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 6th September 1967y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 36.
- 7th September 1967In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 8th September 1967The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 9th September 1967On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th September 1967x = 87 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th September 1967Make x the subject of 5x + 2 = y(x + 2).
- 12th September 1967A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 13th September 1967In a vector proof you find that vector PQ = 3a + 5b and vector RS = 15a + 25b. What does this show about PQ and RS?
- 14th September 1967A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 15th September 1967A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 16th September 1967A car covers 160 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th September 1967Write 6/(x + 5) + 2/(x - 5) as a single fraction.
- 18th September 1967y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 19th September 1967A cuboid measures 6 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th September 1967A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st September 1967On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd September 1967Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 23rd September 1967Solve 15x^2 - 14x - 8 = 0.
- 24th September 1967y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 25th September 1967A cuboid measures 9 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th September 1967A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th September 1967A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 28th September 1967Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 29th September 1967f(x) = 5x - 11. Work out the inverse function f^-1(x).
- 30th September 1967y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 36.