Correct answer: 1000. (100)^1.5 = 100¹ × 100^½ = 100 × 10 = 1000.
Background: 1.5 = 1 + 1/2, and the power 1/2 means square root.
Did you know? (100)^1.5 can also be written as 10³.
Memory trick: 100 × √100 = 1000.
Correct answer: 30. Kyle ate 24 + 21 = 45 lb against John’s 35 lb. The extra is 10 lb, and 10 ÷ 35 × 100 ≈ 28.57%, which is nearly 30%.
Background: Percentage more = (extra ÷ original) × 100.
Did you know? Always divide by the original amount (John’s).
Memory trick: Extra ÷ John’s total.
Correct answer: 500. With B boys and G girls: 0.20B + 0.15G = 90 and 0.80B = 0.85G + 70. Solving gives B = 300 and G = 200, so the total is 500.
Background: Make two equations from the two facts and solve them.
Did you know? Check: failed = 60 + 30 = 90; passed = 240 boys and 170 girls, a difference of 70.
Memory trick: Two facts → two equations.
Correct answer: 1000π cm³. Volume = (1/3)πr²h = (1/3)π(10)²(30) = 1000π cm³.
Background: The volume of a cone is one-third of the cylinder with the same base and height.
Did you know? A cylinder with these measurements has volume πr²h = 3000π.
Memory trick: Cone = 1/3 of cylinder.
Correct answer: 36 km/h. 50 minutes = 5/6 hour, so speed = 30 ÷ (5/6) = 36 km/h.
Background: Convert the time to hours before using speed = distance ÷ time.
Did you know? Divide minutes by 60 to get hours.
Memory trick: Minutes ÷ 60 → hours.
Correct answer: 5√2. Distance = √[(−5 − 0)² + (0 − 5)²] = √50 = 5√2.
Background: Use the distance formula: √[(x₂ − x₁)² + (y₂ − y₁)²].
Did you know? It comes from the Pythagorean theorem.
Memory trick: Square the differences, add, root.
Correct answer: 84/9. 9x − 12 = 72, so 9x = 84 and x = 84/9.
Background: Write the statement as an equation.
Did you know? 84/9 = 28/3, about 9.33.
Memory trick: Add 12 first, then divide by 9.
Correct answer: 3x − 2. Divide each term by 3x: 9x²/3x = 3x and 6x/3x = 2, so the answer is 3x − 2.
Background: Divide each term in the numerator by the denominator separately.
Did you know? You can also factorise: 3x(3x − 2) ÷ 3x.
Memory trick: Cancel 3x.
Correct answer: No solution. The discriminant is D = (−√5)² − 4(2)(1) = 5 − 8 = −3, which is negative, so there is no real solution.
Background: A quadratic has no real roots if D < 0.
Did you know? The equation has two complex roots.
Memory trick: D < 0 → no real roots.
Correct answer: 1. First multiply: 1/3 × 3/2 = 1/2. Then divide by 1/2: 1/2 × 2/1 = 1.
Background: Follow BODMAS: multiplication and division go from left to right.
Did you know? Dividing by a fraction means multiplying by its reciprocal.
Memory trick: Multiply first, then flip and multiply.
Correct answer: Decreases. tan(angle) = height ÷ shadow length. A longer shadow gives a smaller tangent, so the angle decreases.
Background: The Sun is lower in the sky when the shadows are long.
Did you know? Shadows are longest in the early morning and evening.
Memory trick: Longer shadow → lower Sun.
Correct answer: 1¼. Number of boxes = 30 ÷ 24 = 5/4 = 1¼ boxes.
Background: Divide the total by the number in one box.
Did you know? This means one full box and 6 chocolates left over.
Memory trick: 30 ÷ 24 = 1.25.
Correct answer: RAM. RAM is the main (primary) memory that the CPU uses to run programs quickly.
Background: More RAM helps a computer run more programs smoothly.
Did you know? RAM loses its data when the power is off.
Memory trick: RAM = speed.
Correct answer: Google Drive. Google Drive stores files online in the cloud.
Background: Other examples are Dropbox and OneDrive.
Did you know? Cloud files can be opened from any device with internet.
Memory trick: Drive = cloud storage.
Correct answer: John Blankenbaker. John Blankenbaker built the Kenbak-1 in 1971, which is often called the first personal computer.
Background: Only about 40 Kenbak-1 machines were sold.
Did you know? The Apple I and IBM PC came later.
Memory trick: First PC = Kenbak-1.
Correct answer: BCC. BCC (Blind Carbon Copy) sends a copy without showing those addresses to others.
Background: Use BCC when sending to many people to protect privacy.
Did you know? BCC stands for Blind Carbon Copy.
Memory trick: BCC = Blind = hidden.
Correct answer: Dennis Ritchie. Dennis Ritchie created the C language at Bell Labs in the early 1970s.
Background: C was used to write the UNIX operating system.
Did you know? C++ was built on C.
Memory trick: C = Ritchie.
Correct answer: Developing web pages. HTML (HyperText Markup Language) is used to build web pages.
Background: HTML uses tags such as <p> and <h1>.
Did you know? CSS adds style and JavaScript adds action to web pages.
Memory trick: HTML = web page structure.
Correct answer: Encrypted. Ransomware encrypts the victim’s files and demands money to unlock them.
Background: The name comes from “ransom”, money demanded for release.
Did you know? Regular backups are the best protection.
Memory trick: Ransom → files locked (encrypted).
Correct answer: Allow data to bypass the CPU. DMA lets devices transfer data directly to or from memory without going through the CPU.
Background: This frees the CPU to do other work.
Did you know? Disk drives and sound cards often use DMA.
Memory trick: DMA = direct, no CPU middleman.
Correct answer: An operating system technique that allows more than one program to run concurrently. Multiprogramming keeps several programs in memory so the CPU can switch between them and stay busy.
Background: It improves CPU use.
Did you know? Time sharing is an extension of multiprogramming.
Memory trick: Multi = many programs at once.
Correct answer: Minimize data redundancy. Normalization organises tables to reduce repeated (redundant) data.
Background: It splits large tables into smaller related ones.
Did you know? Common forms are 1NF, 2NF, and 3NF.
Memory trick: Normalize = less repetition.
Correct answer: Zero. A photon is a particle of light with zero rest mass.
Background: Photons carry energy and momentum but have no rest mass.
Did you know? They travel at the speed of light.
Memory trick: Photon = massless.
Correct answer: Catalyst. Enzymes are biological catalysts that speed up reactions without being used up.
Background: Most enzymes are proteins.
Did you know? Enzymes work best at a certain temperature and pH.
Memory trick: Enzyme = biological catalyst.
Correct answer: Chromosome. Down syndrome results from an extra copy of chromosome 21, so it is a chromosomal abnormality.
Background: Chromosomes carry genes, which are made of DNA.
Did you know? A normal human cell has 46 chromosomes.
Memory trick: Down = extra chromosome 21.