Daily Practice · Higher Plus
October 1973 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1973 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1973A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 2nd October 1973Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 3rd October 1973Solve x^2 + 3x - 10 < 0.
- 4th October 1973y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 5th October 1973In 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.
- 6th October 1973The probability of winning a game is 3/8. A player expects 9 wins. How many games did they play?
- 7th October 1973On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th October 1973A block has mass 520 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th October 1973Write x^2 + 4x + 15 in the form (x + a)^2 + b.
- 10th October 1973y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 11th October 1973In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 12th October 1973A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 13th October 1973A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 14th October 1973x = 71 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th October 1973Work out the coordinates of the turning point of y = x^2 + 8x - 3.
- 16th October 1973y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 16.
- 17th October 1973A cuboid measures 7 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th October 1973A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th October 1973On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th October 1973A car covers 770 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st October 1973Simplify (x^2 + 2x - 35)/(x - 5).
- 22nd October 1973A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd October 1973A cuboid measures 10 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th October 1973A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th October 1973A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 26th October 1973Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 27th October 1973In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
- 28th October 1973y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 29th October 1973The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 30th October 1973A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 31st October 1973On 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?