Daily Practice · Higher Plus
October 1968 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1968In 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.
- 2nd October 1968The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 3rd October 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 4th October 1968Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 5th October 1968Work out the coordinates of the turning point of y = x^2 - 4x - 13.
- 6th October 1968y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 7th October 1968In a vector proof you find that vector PQ = 2a + 3b and vector RS = 8a + 12b. What does this show about PQ and RS?
- 8th October 1968A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 9th October 1968On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th October 1968Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 11th October 1968Simplify (x^2 - 9x + 8)/(x - 1).
- 12th October 1968y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 13th October 1968A cuboid measures 11 cm by 13 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th October 1968A 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?
- 15th October 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 16th October 1968A rectangle is 30 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th October 1968In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 18th October 1968y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 49.
- 19th October 1968A cuboid measures 8 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th October 1968A 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?
- 21st October 1968On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd October 1968Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 23rd October 1968Make x the subject of 6x + 3 = y(x + 3).
- 24th October 1968A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 25th October 1968The 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.
- 26th October 1968A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 27th October 1968A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 28th October 1968A block has mass 410 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th October 1968Write 6/(x - 2) + 3/(x - 6) as a single fraction.
- 30th October 1968y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 31st October 1968In 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.