Daily Practice · Higher Plus
October 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2004Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 2nd October 2004Solve x^2 + 4x - 12 < 0.
- 3rd October 2004A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 4th October 2004A cuboid measures 3 cm by 8 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th October 2004A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th October 2004A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 7th October 2004Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 8th October 2004Write x^2 + 14x + 15 in the form (x + a)^2 + b.
- 9th October 2004y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 10th October 2004A cuboid measures 14 cm by 4 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th October 2004A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th October 2004On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th October 2004A rectangle is 15 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th October 2004Work out the coordinates of the turning point of y = x^2 + 12x - 4.
- 15th October 2004y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 16th October 2004The 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.
- 17th October 2004A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 18th October 2004A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 19th October 2004Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 20th October 2004Simplify (x^2 - 4x - 21)/(x - 7).
- 21st October 2004y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
- 22nd October 2004In 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.
- 23rd October 2004The probability of winning a game is 3/5. A player expects 60 wins. How many games did they play?
- 24th October 2004On 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?
- 25th October 2004A block has mass 860 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th October 2004In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 27th October 2004A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 28th October 2004In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?
- 29th October 2004A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 30th October 2004A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 31st October 2004x = 130 and y = 30, each correct to the nearest whole number. Work out the upper bound of x - y.